Question: $f(x) = -x^{2}-7x$ $g(t) = t^{3}-3t^{2}+5t+5(f(t))$ $h(t) = 5t^{3}-6t^{2}+5t+f(t)$ $ f(h(1)) = {?} $
First, let's solve for the value of the inner function, $h(1)$ . Then we'll know what to plug into the outer function. $h(1) = 5(1^{3})-6(1^{2})+(5)(1)+f(1)$ To solve for the value of $h$ , we need to solve for the value of $f(1)$ $f(1) = -1^{2}+(-7)(1)$ $f(1) = -8$ That means $h(1) = 5(1^{3})-6(1^{2})+(5)(1)-8$ $h(1) = -4$ Now we know that $h(1) = -4$ . Let's solve for $f(h(1))$ , which is $f(-4)$ $f(-4) = -(-4)^{2}+(-7)(-4)$ $f(-4) = 12$